Arpitha factors out the greatest common factor, 9n, from the terms of the polynomial shown. 162m3n4 + 45n = 9n(_______ + 5)

Given:

162m^3n^4 + 45n = 9n(_______ + 5)

Complete the factored equation.

Solution:

In order complete the factored equation, we simply needed to divide 9n from 162m^3 n^4.

= 162m^3n^4/9n

= 18m^3n^3

= 9n(18m^3n^3 + 5)

Final answer:

= 9n(18m^3n^3 + 5)

When we "factor out" something, we are finding what is common in each term and taking it out to make the expression simpler. It's like if we have 6 apples and 9 apples, we can say we have "3 groups of 2 apples and 3 groups of 3 apples."

In this case, both terms in the expression had 9n in them, so Arpitha took it out to make the expression simpler.

And so by taking the 9n out, we find that inside the parentheses we have a simpler expression, 18m^3n^3+5, which is much easier to look at and work with!

By practicing this method, middle school students learn to simplify big, scary-looking expressions into smaller, manageable pieces. This is a super useful skill in algebra and will help them solve more complex problems as they learn more math.